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Approximation theorems for compactifications

Kotaro Mine (2011)

Colloquium Mathematicae

We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of ℝ n + 1 . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder...

Arbitrage and pricing in a general model with flows

Jan Palczewski (2003)

Applicationes Mathematicae

We study a fundamental issue in the theory of modeling of financial markets. We consider a model where any investment opportunity is described by its cash flows. We allow for a finite number of transactions in a finite time horizon. Each transaction is held at a random moment. This places our model closer to the real world situation than discrete-time or continuous-time models. Moreover, our model creates a general framework to consider markets with different types of imperfection: proportional...

A-realcompact spaces.

Jorge Bustamante, José R. Arrazola, Raúl Escobedo (1998)

Revista Matemática Complutense

Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.

Arens regularity of module actions

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual ( n ) of . Banach algebras for which Z( **) = but ⊊ Z t ( * * ) are...

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